Deleterious effects such as surface heating and turning moments can arise as a consequence of the impingement of thruster plumes with spacecraft surfaces. Such thrusters are normally fired for attitude control. The prediction of such effects must be undertaken at the design stage of the vehicle. In this study, the modelling of such plumes was undertaken. The following prediction techniques were implemented into computer programmes: (a) the Simons model, (b) the Method of Characteristics (MOC), and (c) the Direct Simulation Monte Carlo method (DSMC). The first two methods are derived from continuum equations whilst the third adopts a discrete particle approach. Several DSMC schemes exist for treating the collisional behaviour of the gas, and it was unclear which would be best suited for the intended application. A thorough assessment of the implementation and performance of several such schemes was therefore completed. Having determined the most suitable DSMC scheme, the three modelling techniques were then applied to the isentropic core expansion of a small hydrazine thruster plume. It was found that significant errors occur in the determination of impingement quantities through application of the continuum methods in the flow regime lying between the continuum and free molecular limits. The DSMC technique was also used to calculate the nozzle lip and backflow expansion regions of the same hydrazine thruster. A significant degree of backflow was found with flow angles of up to 140º. The sensitivity of the calculations to the conditions initially assumed were assessed and found to be important.